Physical Chemistry , 1st ed.

6.36.Figure 6.16 is the phase diagram of^3 He at very low
temperatures:

Figure 6.16 Phase diagram of^3 He.Source:Adapted from W. E. Keller,
Helium-3 and Helium-4,Plenum Press, New York, 1969.

Notice that the slope of the solid-liquid equilibrium line below
about 0.3 K is negative. Interpret this surprising experimental
finding.

6.37.If a phase diagram were designed to have only a single
axis, what would be the form of the phase rule for a single com-
ponent? How many parameters would you have to specify to
indicate the conditions of (a)a phase transition, or (b)the crit-
ical point?

6.38.If a material sublimes at normal atmospheric pressure,
does one need higher or lower pressures to get that material
in a liquid phase? Justify your answer.

6.39.Defining the critical point of a substance requires two
degrees of freedom. (Those degrees of freedom are the criti-
cal temperature and the critical pressure.) Justify this fact in
light of the Gibbs phase rule.

6.40.Refer to Figure 6.3, the unexpanded version of the
phase diagram of H 2 O. Label each line in the phase diagram
in terms of what derivative it represents.

6.41.Repeat the previous exercise, only this time using Figure
6.6, the more complete phase diagram for H 2 O.

Temperature (K)

Pressure (atm) Liquid

Solid I

Solid III

Solid II

Gas

0.32 17.8

28.9

6.42.The phase diagram for elemental sulfur is shown in

Figure 6.17.

Figure 6.17 Phase diagram of elemental sulfur.

(a)How many allotropes are shown? (b)What is the stable

allotrope of sulfur under normal conditions of temperature

and pressure? (c)Describe the changes to sulfur as its tem-

perature is increased from 25°C while at 1 atm pressure.

6.43.Consider the phase diagram of sulfur in the previous

exercise. If one starts at 25°C and 1 atm pressure (which is

about equal to 1 bar) and increases the temperature, com-

ment on the entropy change as the sulfur goes from rhombic

to monoclinic solid phases. Is it positive or negative? On the

basis of the second law of thermodynamics, is the phase tran-

sition expected to be spontaneous?

6.44.Rearrange the Clausius-Clapeyron equation, equation

6.14, in terms of the pressure p 2 of a material. Plot the

vapor pressures of H 2 O (the boiling point is 100°C, vapH

40.71 kJ/mol), neon (the boiling point is 246.0°C, vapH

1.758 kJ/mol), and Li (the boiling point is 1342°C,

vapH134.7 kJ/mol). Although these three materials are

very different, are there any similarities in the behavior of

the vapor pressures as the temperature increases?

Temperature (K)

Pressure (atm)

Rhombic

Liquid

Gas

Mono-

clinic

298

1

Exercises for Chapter 6 165

Symbolic Math Exercises